The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts,...
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The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and “play” with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at www.monroecc.edu/wusers/pseeburger/.Broader Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly “see” how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.

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This website is a project by Marc Renault, supported by Shippensburg University. The goal is to make a complete library of...
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This website is a project by Marc Renault, supported by Shippensburg University. The goal is to make a complete library of Geogebra applets for Calculus I that are suitable for in-class demonstrations and/or student exploration.

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The readings on this web site were designed as part of the IT Multivariable Calculus and Vector Analysis course at the...
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The readings on this web site were designed as part of the IT Multivariable Calculus and Vector Analysis course at the University of Minnesota. Students in this course are expected to read some of these documents (those marked with an asterisk * in the lecture list) before attending the lecture on the topic. The intent was to allow lecturers in the course spend more lecture time helping students understand and apply the material and less time on simply presenting the theory.The remaining pages are a loosely organized collection of lecture notes, example problems, and other resources for students in the course. As no effort has been made to turn this into a comprehensive source of information on multivariable calculus and vector analysis, the coverage of different topics is uneven, with some important topics (such as Lagrange multipliers) missing altogether. Moreover, some of the readings not marked by asterisks assume content that is presented in lecture and not in the online readings. Nonetheless, I hope that what is available will be helpful for those trying to learn multivariable calculus and vector analysis.One can view these readings more like a lecture than a textbook. They are not a replacement of a mathematics textbook because they don't cover all the theoretical details behind the main ideas. For the same reason, they should be easier to understand than a textbook. Many of the readings contain interactive graphics that I term concept visualization tools (or CVTs).

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